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# m03 # 11 question

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m03 # 11 question [#permalink]  29 Jun 2011, 05:52
If x is an integer, is x even?

1. 11/x is an integer
2. 22/x is an integer

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Re: m03 # 11 question [#permalink]  29 Jun 2011, 05:55
(1) says

11/x is an integer

We know that 11 is a prime, so it can be divisible only by 1 or 11, so x = 1 or 11

=> x is odd, and the answer to the question is a definite No.

Thus (1) is Sufficient

(2) says 22/x is integer, but now x can be 1,2,11,22

=> x can be odd/even

So (2) is not sufficient

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Re: m03 # 11 question [#permalink]  26 Feb 2012, 15:16
Why couldn't X be zero? 11/0 = 0 which is an even integer. That would make the answer E.
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Re: m03 # 11 question [#permalink]  26 Feb 2012, 15:35
Expert's post
hummcon wrote:
Why couldn't X be zero? 11/0 = 0 which is an even integer. That would make the answer E.

Division by zero is undefined, so 11/0 is not allowed. The question should mention that x does not equal to zero to avoid confusion. It will be corrected for the next edition.

For more on number properties check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: m03 # 11 question   [#permalink] 26 Feb 2012, 15:35
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# m03 # 11 question

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